Table of contents

Simple approximate expressions are derived for the coefficient C₈ of the R^-8 term in certain long-range atom-atom interactions. The resulting values of C₈ for K-Kr and K-Xe interactions are consistent with the total cross-section measurements of Beck and Loesch. The limitations of the oscillator model for the calculation of C₈ are discussed.

We describe the numerical method used on a general programme for the solution of the Hartree-Fock equations in the calculation of radial wave functions for atomic configurations.

Calculations are performed of the lifetimes of the 1s2s2p ⁴P_5/2 states of He^- and lithium, which decay through the spin-spin interaction, using wave functions consisting of some thirty superposed configurations. Agreement with experiment is good in the case of lithium, but the theoretically predicted lifetime of He^- is thirty times larger than that observed.

Asymptotic phases and amplitudes for positive energies of the spherical Coulomb functions are defined for each value of the angular momentum quantum number L. Recurrence relations are established for each pair of these entities differing by one unit in L. Analytical expressions for S-wave phases and amplitudes are obtained by an iterative method analogous to the WKB approximation. A short table of the asymptotic phases calculated at two distinct points in the asymptotic region is given for different values of L and the wave number (including zero). The accuracy of the numerical results is discussed.

A generalized impact parameter formalism for heavy-particle collisions is developed in a rigorous way from a purely quantal formalism in which all quantities, which tend uniformly to a limit as the mass of the atomic nuclei becomes infinite, are replaced by that limit. Subsequently, an expression for the differential scattering cross section is derived in terms of quantities obtained from impact parameter calculations. In particular, this expression is used to calculate the probability of charge exchange at large angles of scattering for protons in hydrogen. It is shown that our formalism predicts the correct damping of the oscillations in the probability at low energies of impact.

Impulse approximation cross sections are evaluated for the electron capture processes

H⁺ + H(1s) -> H(2p, 3s or 3p) + H⁺

He²⁺ + H(1s) -> He⁺ (2p or 3s) + H⁺

The results for capture into the 2p state of atomic hydrogen are in close agreement with the measurements of Stebbings et al. in 1965. Total impulse approximation cross sections for capture by protons and alpha particles are estimated. The proton impact cross sections are practically identical with estimates by Coleman and McDowell based on less reliable data.

In general, atomic potentials are long range in nature and may affect the short-range threshold law of Wigner. In order to solve the threshold problem for atomic collisions generally, i.e. including long-range coupling between both degenerate as well as non-degenerate channels, one must first devise methods of obtaining accurate asymptotic solutions of the radial scattering equations. In the present paper we develop a method of obtaining such solutions in the asymptotic region for energies very near to the excitation thresholds.

Results of solving the threshold problem in several model cases, using the present method, will be reported in a second paper.

The method developed in a previous paper has been used to determine the effect of long-range dipole forces on the threshold behaviour of cross sections for three different mathematical models.

Results are obtained for systems with degenerate as well as non-degenerate channels. It is found that for the non-degenerate case the α/r² potentials do not alter Wigner's law for short-range forces. However, the range of energy over which the short-range behaviour is maintained decreases progressively with the decrease of energy difference between the non-degenerate levels.

For the exactly degenerate case Wigner's law is violated and the cross section tends to a finite value at the threshold.

The first Born approximation is used to calculate the cross section for electron excitation of the ground state of helium to the 2 ¹P state. Various ground-and excited-state wave functions are employed and the calculations are performed using both the length and velocity formulations of the Born approximation integrals. The most accurate calculations give a first Born cross section which is accurate to better than 2%. The total and differential cross sections are compared with experiment; the agreement is good.

A six-parameter ground-state wave function and modified hydrogenic excited-state wave functions are used to calculate the first Born approximation cross section for electron excitation of the ground state of helium to the n¹P (n = 2 to 6) and n¹D (n = 3 to 6) states. Calculations are carried out using both the length and velocity formulations of the Born approximation integrals and these show that the total cross sections are accurate to about 4%. The total and differential cross sections are compared with other calculations and with experiment. At large electron impact energies the theoretical and experimental total cross sections do not agree.

The first Born approximation cross sections for proton excitation of the ground state of helium to the n¹P (n = 2 to 6) and n¹D (n = 3 to 6) states are calculated using a six-parameter ground-state wave function and modified hydrogenic excited-state wave functions. To determine the accuracy of the results, both the `length' and `velocity' formulations of the Born approximation integrals were evaluated, and these indicate that the approximate Born cross sections are within about 4% of the exact Born cross sections. A comparison of these cross sections is made with recent theoretical and experimental results. In general, the agreement between theory and experiment is not good.

The attenuation of a fast beam of helium atoms by electron-loss collisions during passage through hydrogen has been carefully investigated. The measurements allow the metastable atom population of the beam to be determined and, for the first time, permit separate measurements of the electron-loss cross sections for both ground-state and metastable helium atoms. At 120 kev these are 7.3 ± 0.8 and 48 ± 8 cm² × 10^-17 respectively.

Absolute cross sections have been measured for the emission of certain spectral lines of atomic and molecular oxygen induced during the passage of protons through molecular oxygen. The cross sections for the population of the vprime = 0 and vprime = 1 levels of the O₂⁺(b ⁴Σ) excited state are, respectively, 1.33 × 10^-17 and 0.95 × 10^-17 cm² at 150 keV and decrease towards higher energies. The ratio of these two populations is in reasonable agreement with a value of 1.21 obtained by Wacks using calculated Franck-Condon probabilities.

Cross sections have been measured for the reaction Na⁺ +e -> Na²⁺ +2e for electrons with energies between threshold and 3500 ev. Similar cross sections of K⁺ ions have also been measured for electron energies up to 3000 ev. The errors are estimated to be less than ±6% over a wide range of electron energies and the results agree with those of Hooper et al., which were confined to electron energies up to 1000 ev.

We present simple formulae for use in calculating the electron-impact widths of isolated lines emitted by ionized species in cases where Debye shielding may be of importance. The various approximations made are discussed in conjunction with application of the formulae to some experimental results for singly and multiply ionized species.

Transverse birefringence has been observed in an aligned spin assembly consisting of helium 4 atoms in the metastable state 2 ³S₁. The alignment of the spins was produced by optical pumping with unpolarized light. Using a cross-beam of off-resonant radiation, for example from a helium 3 lamp, together with a suitable combination of polarizer and analyser, birefringence signals could be displayed analogous to the absorption signals conventionally used for the optical monitoring of magnetic resonance.

An analysis of the phenomenon is given, showing quite generally that birefringence monitors separately the degree of alignment of the spin assembly, even when orientation is also present; the latter can be monitored by the magnetic rotation of the plane of polarization for axial light. The analysis also includes the effect of the spectral characteristics of the monitoring lamp, i.e. the central frequencies of emission and the Doppler width, on the strengths of absorption and birefringence signals displayed by optically thin samples.

King furnace spectra of CaH and CaD at temperatures greater than 1200 °c have been obtained in absorption. Five new bands of CaH at 2815 Angstrom, 2752 Angstrom, 2609 Angstrom, 2580 Angstrom, 2535 Angstrom and two new bands of CaD at 2711 Angstrom and 2646 Angstrom have been measured and analysed. Of these, the two CaD bands and the first three CaH bands have been shown to be extensions of some of the systems already reported. The CaH bands at 2580 Angstrom and 2535 Angstrom, however, have been analysed as the (0, 0) bands of two different systems, which may be called H ²Σ -> X ²Σ and I ²Σ -> X ²Σ transitions, respectively. Rotational constants have also been calculated where necessary.

The fluorescence response functions of oxygen-free benzene solutions containing 3 × 10^-3 M anthracene and concentrations of up to 1·2 × 10^-3 M perylene were observed using the phase and modulation fluorometer. The response functions of the directly excited anthracene and perylene fluorescence are simple exponential decay functions, while that of the perylene fluorescence, indirectly excited by energy transfer from anthracene, is the difference of the two exponential decay functions. Stern-Volmer kinetics are applicable because of the statistical `mixing' of the molecules by diffusion, which increases the effective critical dipole-dipole transfer radius from 31 Angstrom to 43 Angstrom.

The rotational analysis of the 0-0, 1-1, 0-1 and 1-2 bands of the γ system of SiF has been completed. The upper state C is most probably²Δ (case b). Derived constants for this state, in units of cm^-1, are as follows:

T₀₀ = 39 537.45 (relative to ײII_1/2)

ΔG_1/2 = 878.38

B₀ = 0.600 68

α = 0.005 39

A₀ = 2.46.

The rotational analysis of three bands of the g-a system of S₂ has been completed. The transition is ¹Δ_u-¹Δ_g, and the lower state is also the lower state of the system f¹Δ_u-a¹Δ_g. Constants for the three states are as follows:

State	T0 0	ωe	xeωe	Be	103αe
g 1Δu	52444·7 + a	816·4	2·7	0·3217	1·44
f 1Δu	36743·5 + a	438·13	2·655	0·2273	1·77
a 1Δg	a	701·94	3·015	0·2928	1·79

The singlet states of S₂ are briefly reviewed and compared with those of O₂. If f ¹Δ_u is stable in O₂, the 0-0 band of f ¹Δ_u-a¹Δ_g should lie at about 1960 Angstrom.

Electron spin resonance has been observed at 280 MHz in irradiated ice and irradiated frozen hydrogen peroxide solutions. In polycrystalline ice a doublet splitting of 26 ± 1 gauss was observed which is considerably smaller than the value of about 40 gauss recorded at 9.5 GHz. This difference has been shown to arise from anisotropy of the g value. In a 70 wt% hydrogen peroxide glass the half-power linewidth obtained after the removal of spin-spin broadening by annealing was 7.5 ± 1 gauss, in good agreement with the theoretica value. The ΔM = 2 transition was also observed in a hydrogen peroxide glass at 280 MHz, and the ratio of the intensity of this transition to the normal ΔM = 1 transition was in reasonable agreement with the value predicted from high-frequency measurements.

Term values and oscillator strengths in highly ionized ions of the iron period are calculated via the Slater theory of atomic structure and are used to identify laboratory spectra of 3s² 3pⁿ-3s² 3p^n-1 4s, 5s, 4d, 5d transitions in the argon, chlorine and sulphur isoelectronic sequences. New classifications are made in argon, scandium, titanium, vanadium, manganese and iron. The isoelectronic data and the theoretical calculations are used to identify lines in the solar spectrum between 50 and 110 Angstrom. The calculated oscillator strengths of resonance transitions in Fe IX to Fe XIV and Ni XI to Ni XIV are tabulated.

The Thomas-Fermi screening function &empty;(x) is shown to be accurately described by the expression 317 × exp(-6.62x^1/4) in the range 0.3 < x < 16. The consequent form of the Thomas-Fermi electron density distribution is derived, and Firsov's atomic interaction potential is shown to have the form E = B exp(-αr^1/4), where B and α are constants of known Z dependence and r is the internuclear distance.

It is also suggested that a potential of the type E' = A' exp(-k'r^1/3) gives a better representation of the interaction potential over a wider range of energies and distances, and explicit values of A' and k' are given for copper-copper interactions. However, the Z dependence of A' and k' is not obvious.

It is shown that, contrary to the view expressed in their paper, the work of McCarroll and Salin does not constitute a derivation of the exact asymptotic energy dependence of the cross section for resonant electron capture by protons from atomic hydrogen.

We report calculations of the Stark broadening parameters of two singly ionized argon multiplets as a function of electron temperature. Our results show that for most experimental conditions the broadening parameters are relatively independent of temperature, contrary to earlier predictions, and in reasonable agreement with available experimental measurements.

In the Morse empirical relationship between bond length and frequency, viz. vL³ = l similar, equals 3000, and the modified relationships due to Clark, viz.vL³ radicaln = K, and Allenet al., viz. vL³ radicalμ =Kprime, the constants l, K, and Kprime never remain constant for a di-atom in all types of species. The proposed empirical relationship

νL³n/(m₁+m₂)^1/2=Asime 5500

fits the experimental data satisfactorily and is of general validity, the constant A remaining constant for a di-atom in all types of species.

The effect of electron exchange on the cross sections for excitation of the ground state of helium to n¹P and n¹D states by electron impact is investigated by employing the Rudge and Ochkur approximations to the exchange scattering amplitude. Comparison is made with experimental data and it is found that the inclusion of exchange in these approximations does not remove the existing discrepancies between theory and experiment at medium impact energies.